Information on Result #599740
There is no digital (28, 117, 226)-net over F5, because extracting embedded orthogonal array would yield linear OA(5117, 226, F5, 89) (dual of [226, 109, 90]-code), but
- construction Y1 [i] would yield
- OA(5116, 143, S5, 89), but
- the linear programming bound shows that M ≥ 2738 237588 593697 454668 762256 522048 887080 570758 264064 445890 203342 535984 543104 632393 806241 452693 939208 984375 / 2 228541 507840 976583 547528 > 5116 [i]
- OA(5109, 226, S5, 83), but
- discarding factors would yield OA(5109, 147, S5, 83), but
- the linear programming bound shows that M ≥ 97832 005097 623965 961965 091455 398251 491670 818930 622769 438002 739592 061328 226246 796901 932611 945085 227489 471435 546875 / 5 803319 642355 292721 815985 390811 721467 > 5109 [i]
- discarding factors would yield OA(5109, 147, S5, 83), but
- OA(5116, 143, S5, 89), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (28, 118, 226)-net over F5 | [i] | m-Reduction | |